This notebook is for the acoustic analysis of the falling diphthongs in the standard Mandarin with the approach GAMMs.

#install.packages('rmarkdown')
# Importation des emballages 
#install.packages("itsadug")

library(ggplot2)
library(mgcv)
## Loading required package: nlme
## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.
library(itsadug)
## Loading required package: plotfunctions
## 
## Attaching package: 'plotfunctions'
## The following object is masked from 'package:ggplot2':
## 
##     alpha
## Loaded package itsadug 2.4 (see 'help("itsadug")' ).
source("gamm_hacks.r")
#install.packages("tidyverse")
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ tibble  3.1.0     ✓ dplyr   1.0.5
## ✓ tidyr   1.1.3     ✓ stringr 1.4.0
## ✓ readr   1.4.0     ✓ forcats 0.5.1
## ✓ purrr   0.3.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x plotfunctions::alpha() masks ggplot2::alpha()
## x dplyr::collapse()      masks nlme::collapse()
## x dplyr::filter()        masks stats::filter()
## x dplyr::lag()           masks stats::lag()

After the importation of the packages, let’s read the data.

# Importation des données 

au <- read.table(file="au0b.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ai <- read.table(file="ai0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ei <- read.table(file="ei0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ou <- read.table(file="ou0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)

Change of the nature of the variables in the dataset.

The criterion is that all the numerical variables are numerated and the string varibles are factored.

1 /ai/

Lets start from /ai/:

ai$sexe<-as.factor(ai$sexe)
ai$ton<-as.factor(ai$ton)
ai$pow<-as.factor(ai$pow)
ai$contexte.D<-as.factor(ai$contexte.D)
ai$contexte.G<-as.factor(ai$contexte.G)

ai$f1<-as.numeric(ai$f1)
## Warning: NAs introduced by coercion
ai$f2<-as.numeric(ai$f2)
## Warning: NAs introduced by coercion
ai$f3<-as.numeric(ai$f3)
## Warning: NAs introduced by coercion
ai$f0<-as.numeric(ai$f0)
## Warning: NAs introduced by coercion
head(ai)
##   numero sexe locuteur diphtongue ton pow contexte.G contexte.D duree.ms.
## 1      1    F     FS11         ai   4   f          h          0  102.6625
## 2      1    F     FS11         ai   4   f          h          0  102.6625
## 3      1    F     FS11         ai   4   f          h          0  102.6625
## 4      1    F     FS11         ai   4   f          h          0  102.6625
## 5      1    F     FS11         ai   4   f          h          0  102.6625
## 6      1    F     FS11         ai   4   f          h          0  102.6625
##   measurement.no       f1       f2       f3       f0
## 1              0 770.9403 1592.367 2791.365 242.7606
## 2              1 789.5770 1654.538 2661.433 232.8865
## 3              2 790.5264 1676.141 2643.341 228.2137
## 4              3 792.7979 1771.876 2587.896 224.4104
## 5              4 786.4961 1814.919 2436.698 219.7656
## 6              5 760.0966 1827.338 2542.548 214.1222

In the dataset we can see the number of the data numero, the gender sexe, the speaker locuteur, the tone ton, the position in the word pow, the context before and after this diphthong contexte.G / contexte.D, the duration of the diphthongs duree.ms. and f0, f1, f2, f3 trajectories, each of them represented by 11 measurements taken at equal intervals (at 0%, 10%, 20%, . . . , 100%).

# Regroupement par les facteurs
ai.mas <- droplevels(subset(ai,sexe=="M"))
ai.fem <- droplevels(subset(ai,sexe=="F"))

1.1 Masculin

1.1.1 F1

Then the trajectories of f1 in different tones with regard of the sexes and the durations.

ggplot(ai.mas, aes(x=measurement.no, y=f1, group=numero,
                     alpha=duree.ms.)) +
  facet_grid(~ton) + geom_line()
## Warning: Removed 28 row(s) containing missing values (geom_path).

ggplot(ai.fem, aes(x=measurement.no, y=f1, group=numero,
                     alpha=duree.ms.)) +
  facet_grid(~ton) + geom_line()
## Warning: Removed 25 row(s) containing missing values (geom_path).

Then the first model with a basic smooth of tone 1 and difference smooths.

ai.mas$ton.ord <- as.ordered(ai.mas$ton)
contrasts(ai.mas$ton.ord) <- "contr.treatment"
ai.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
                        s(measurement.no, by=ton.ord, bs="cr"),
                      data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.diff)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   508.92      20.76  24.514  < 2e-16 ***
## ton.ord2      120.43      22.33   5.393 8.47e-08 ***
## ton.ord3      173.89      23.07   7.536 1.01e-13 ***
## ton.ord4      109.93      21.51   5.110 3.81e-07 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df      F  p-value    
## s(measurement.no)          4.434  5.392  5.263 5.67e-05 ***
## s(measurement.no):ton.ord2 1.017  1.032 10.413  0.00111 ** 
## s(measurement.no):ton.ord3 1.001  1.002  4.728  0.02980 *  
## s(measurement.no):ton.ord4 3.570  4.385  7.968 1.47e-06 ***

Then the plots of predictions and difference smooth.

plot_smooth(ai.mas.gam.diff, view="measurement.no",
            plot_all="ton.ord", rug=F)
## Summary:
##  * ton.ord : factor; set to the value(s): 1, 2, 3, 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * NOTE : No random effects in the model to cancel.
## 

plot_diff(ai.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("1","2")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  0.000000 - 7.575758
plot_diff(ai.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("2","3")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  2.323232 - 10.000000
plot_diff(ai.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("3","4")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  0.000000 - 2.929293
##  6.969697 - 10.000000

The model that accounts for the influence of duree.ms. on the trajectories.

ai.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
                              s(duree.ms., bs="cr") +
                              ti(measurement.no, duree.ms.) +
                              s(measurement.no, by=ton.ord, bs="cr"),
                         data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.dur)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   521.48      20.47  25.471  < 2e-16 ***
## ton.ord2       96.33      22.45   4.291 1.94e-05 ***
## ton.ord3      174.32      22.42   7.777 1.74e-14 ***
## ton.ord4       97.59      21.32   4.578 5.25e-06 ***
## 
## Approximate significance of smooth terms:
##                                edf Ref.df     F  p-value    
## s(measurement.no)            4.526  5.458 2.689   0.0153 *  
## s(duree.ms.)                 5.581  6.507 5.202 3.61e-05 ***
## ti(measurement.no,duree.ms.) 7.258  9.082 4.050 3.73e-05 ***
## s(measurement.no):ton.ord2   2.838  3.498 7.788 1.66e-05 ***
## s(measurement.no):ton.ord3   2.279  2.815 3.364   0.0173 *  
## s(measurement.no):ton.ord4   4.009  4.879 6.286 1.52e-05 ***

The plots with regard the durations.

plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 170. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 80. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.mas.gam.dur, view=c("measurement.no","duree.ms."),
        ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

The model with regard of f0.

ai.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
                              s(f0, bs="cr") +
                              ti(measurement.no, f0) +
                              s(measurement.no, by=ton.ord, bs="cr"),
                         data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.f0)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   515.84      19.38  26.619  < 2e-16 ***
## ton.ord2       98.96      21.39   4.628 4.21e-06 ***
## ton.ord3      133.59      22.60   5.912 4.69e-09 ***
## ton.ord4       99.55      19.87   5.009 6.49e-07 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          5.043  6.028 3.347 0.002781 ** 
## s(f0)                      2.675  3.219 6.283 0.000272 ***
## ti(measurement.no,f0)      3.877  4.994 2.958 0.011798 *  
## s(measurement.no):ton.ord2 3.114  3.839 7.162 2.42e-05 ***
## s(measurement.no):ton.ord3 2.262  2.803 6.325 0.000460 ***
## s(measurement.no):ton.ord4 4.213  5.118 8.474  < 2e-16 ***

The plot of such model.

plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=100),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 100. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=120),
            rug=F, col="orange", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 120. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=140),
            rug=F, col="yellow", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 140. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=180),
            rug=F, col="green", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 180. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=200),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 200. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.mas.gam.f0, view=c("measurement.no","f0"),
        ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

#ai.mas.gam.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
#                           s(f0, bs="cr") +
#                           ti(measurement.no, f0) +
#                           s(measurement.no, by=ton.ord, bs="cr") +
#                           s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
#                         data=ai.mas, method="fREML")

We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.

ai.central<-droplevels(subset(ai,measurement.no>=2))
ai.central<-droplevels(subset(ai.central,measurement.no<=8))

ai.central.mas <- droplevels(subset(ai.central,sexe=="M"))
ai.central.fem <- droplevels(subset(ai.central,sexe=="F"))
ai.central.mas$ton.ord <- as.ordered(ai.central.mas$ton)
contrasts(ai.central.mas$ton.ord) <- "contr.treatment"
ai.central.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                        s(measurement.no, by=ton.ord, bs="cr",k=6),
                      data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.diff)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   472.08      19.51  24.201  < 2e-16 ***
## ton.ord2      171.54      20.96   8.184 1.28e-15 ***
## ton.ord3      225.45      21.68  10.399  < 2e-16 ***
## ton.ord4      187.63      20.19   9.292  < 2e-16 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          2.404  2.924 9.433 1.01e-05 ***
## s(measurement.no):ton.ord2 1.002  1.004 0.147   0.7039    
## s(measurement.no):ton.ord3 1.002  1.005 1.309   0.2530    
## s(measurement.no):ton.ord4 2.529  3.067 2.551   0.0533 .
plot_smooth(ai.central.mas.gam.diff, view="measurement.no",
            plot_all="ton.ord", rug=F)
## Summary:
##  * ton.ord : factor; set to the value(s): 1, 2, 3, 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * NOTE : No random effects in the model to cancel.
## 

plot_diff(ai.central.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("1","2")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  2.000000 - 8.000000
plot_diff(ai.central.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("2","3")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  2.848485 - 8.000000
plot_diff(ai.central.mas.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("3","4")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  2.000000 - 3.030303
##  5.818182 - 8.000000
ai.central.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                              s(duree.ms., bs="cr",k=6) +
                              ti(measurement.no, duree.ms.,k=6) +
                              s(measurement.no, by=ton.ord, bs="cr",k=6),
                         data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.dur)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   483.05      19.43  24.864  < 2e-16 ***
## ton.ord2      153.92      21.26   7.239 1.19e-12 ***
## ton.ord3      225.56      21.26  10.609  < 2e-16 ***
## ton.ord4      175.66      20.20   8.697  < 2e-16 ***
## 
## Approximate significance of smooth terms:
##                                edf Ref.df      F  p-value    
## s(measurement.no)            2.393  2.910 10.314 3.87e-06 ***
## s(duree.ms.)                 4.484  4.852  4.597 0.000297 ***
## ti(measurement.no,duree.ms.) 1.236  1.431  5.669 0.006689 ** 
## s(measurement.no):ton.ord2   1.000  1.000  0.094 0.759550    
## s(measurement.no):ton.ord3   1.000  1.001  1.487 0.223105    
## s(measurement.no):ton.ord4   2.587  3.131  2.965 0.029587 *
plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 170. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 80. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.central.mas.gam.dur, view=c("measurement.no","duree.ms."),
        ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

ai.central.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                              s(f0, bs="cr",k=6) +
                              ti(measurement.no, f0,k=6) +
                              s(measurement.no, by=ton.ord, bs="cr",k=6),
                         data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.f0)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   480.55      18.43  26.068  < 2e-16 ***
## ton.ord2      159.40      20.21   7.886  1.3e-14 ***
## ton.ord3      182.35      21.24   8.583  < 2e-16 ***
## ton.ord4      178.19      18.85   9.455  < 2e-16 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          2.449  2.975 7.785  5.8e-05 ***
## s(f0)                      2.888  3.362 5.997 0.000297 ***
## ti(measurement.no,f0)      1.005  1.010 6.139 0.013357 *  
## s(measurement.no):ton.ord2 1.000  1.000 0.233 0.629530    
## s(measurement.no):ton.ord3 1.000  1.001 0.006 0.938828    
## s(measurement.no):ton.ord4 2.698  3.256 2.878 0.031657 *
plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=100),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 100. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=120),
            rug=F, col="orange", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 120. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=140),
            rug=F, col="yellow", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 140. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=180),
            rug=F, col="green", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 180. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=200),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 200. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.central.mas.gam.f0, view=c("measurement.no","f0"),
        ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

1.1.2 F2

Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.

ggplot(ai.mas, aes(x=measurement.no, y=f2, group=numero,
                     alpha=duree.ms.)) +
  facet_grid(~ton) + geom_line()
## Warning: Removed 28 row(s) containing missing values (geom_path).

ggplot(ai.fem, aes(x=measurement.no, y=f2, group=numero,
                     alpha=duree.ms.)) +
  facet_grid(~ton) + geom_line()
## Warning: Removed 25 row(s) containing missing values (geom_path).

Then we fit the same model with a basic smooth of tone 1 and difference smooths.

ai.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
                        s(measurement.no, by=ton.ord, bs="cr"),
                      data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.diff)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1808.78      25.76  70.213  < 2e-16 ***
## ton.ord2     -190.78      27.71  -6.885 9.73e-12 ***
## ton.ord3     -182.21      28.63  -6.364 2.89e-10 ***
## ton.ord4     -157.18      26.70  -5.887 5.22e-09 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          3.783  4.654 6.929 7.58e-06 ***
## s(measurement.no):ton.ord2 1.000  1.001 0.783    0.376    
## s(measurement.no):ton.ord3 1.001  1.001 0.225    0.635    
## s(measurement.no):ton.ord4 1.004  1.008 0.360    0.550

Now the plots of f2 with different tones.

plot_smooth(ai.mas.f2.gam.diff, view="measurement.no",
            plot_all="ton.ord", rug=F)
## Summary:
##  * ton.ord : factor; set to the value(s): 1, 2, 3, 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * NOTE : No random effects in the model to cancel.
## 

plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("1","2")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  0.000000 - 10.000000
plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("2","3")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  0.000000 - 2.020202
plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("3","4")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.

## 
## measurement.no window(s) of significant difference(s):
##  5.252525 - 10.000000

The model that accounts for the influence of duree.ms. on the trajectories.

ai.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
                              s(duree.ms., bs="cr") +
                              ti(measurement.no, duree.ms.) +
                              s(measurement.no, by=ton.ord, bs="cr"),
                         data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.dur)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1826.36      25.30  72.182  < 2e-16 ***
## ton.ord2     -210.79      27.64  -7.627 5.22e-14 ***
## ton.ord3     -190.56      27.77  -6.861 1.15e-11 ***
## ton.ord4     -178.75      26.32  -6.793 1.81e-11 ***
## 
## Approximate significance of smooth terms:
##                                edf Ref.df      F  p-value    
## s(measurement.no)            3.893  4.783  8.213 6.26e-07 ***
## s(duree.ms.)                 3.903  4.707  5.118 0.000252 ***
## ti(measurement.no,duree.ms.) 2.869  4.012 12.552  < 2e-16 ***
## s(measurement.no):ton.ord2   1.001  1.002  1.332 0.248618    
## s(measurement.no):ton.ord3   1.001  1.003  0.351 0.553691    
## s(measurement.no):ton.ord4   1.001  1.003  0.038 0.847241

The plots with regard the durations.

plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 170. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 80. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
        ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

ai.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
                              s(f0, bs="cr") +
                              ti(measurement.no, f0) +
                              s(measurement.no, by=ton.ord, bs="cr"),
                         data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.f0)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1809.15      24.68  73.316  < 2e-16 ***
## ton.ord2     -187.20      27.28  -6.862 1.21e-11 ***
## ton.ord3     -201.12      28.74  -6.999 4.80e-12 ***
## ton.ord4     -156.85      25.33  -6.191 8.79e-10 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          4.100  5.036 9.733  < 2e-16 ***
## s(f0)                      5.833  6.673 5.023 2.82e-05 ***
## ti(measurement.no,f0)      2.307  2.805 2.708   0.0422 *  
## s(measurement.no):ton.ord2 1.001  1.002 0.005   0.9472    
## s(measurement.no):ton.ord3 1.001  1.001 0.034   0.8553    
## s(measurement.no):ton.ord4 1.004  1.008 0.011   0.9373
plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 100. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
            rug=F, col="orange", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 120. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
            rug=F, col="yellow", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 140. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
            rug=F, col="green", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 180. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; set to the value(s): 200. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.mas.f2.gam.f0, view=c("measurement.no","f0"),
        ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000. 
##  * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

The central portion:

ai.central.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                        s(measurement.no, by=ton.ord, bs="cr",k=6),
                      data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.diff)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1797.78      28.10  63.974  < 2e-16 ***
## ton.ord2     -169.65      30.20  -5.618 2.77e-08 ***
## ton.ord3     -154.65      31.23  -4.952 9.20e-07 ***
## ton.ord4     -136.24      29.09  -4.683 3.38e-06 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F p-value   
## s(measurement.no)          1.005  1.011 7.229 0.00732 **
## s(measurement.no):ton.ord2 1.001  1.002 0.268 0.60543   
## s(measurement.no):ton.ord3 1.001  1.002 0.035 0.85460   
## s(measurement.no):ton.ord4 1.001  1.003 0.595 0.44147
plot_smooth(ai.central.mas.f2.gam.diff, view="measurement.no",
            plot_all="ton.ord", rug=F)
## Summary:
##  * ton.ord : factor; set to the value(s): 1, 2, 3, 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * NOTE : No random effects in the model to cancel.
## 

plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("1","2")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  2.000000 - 8.000000
plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("2","3")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## Difference is not significant.
plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("3","4")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  6.242424 - 8.000000
plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
          comp=list(ton.ord=c("2","4")))
## Summary:
##  * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.

## 
## measurement.no window(s) of significant difference(s):
##  3.939394 - 7.454545
ai.central.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                              s(duree.ms., bs="cr",k=6) +
                              ti(measurement.no, duree.ms.,k=6) +
                              s(measurement.no, by=ton.ord, bs="cr",k=6),
                         data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.dur)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1809.11      27.47  65.867  < 2e-16 ***
## ton.ord2     -178.42      29.78  -5.992 3.30e-09 ***
## ton.ord3     -158.81      30.29  -5.243 2.09e-07 ***
## ton.ord4     -152.09      28.53  -5.331 1.32e-07 ***
## 
## Approximate significance of smooth terms:
##                                edf Ref.df     F  p-value    
## s(measurement.no)            1.106  1.204 6.368  0.01168 *  
## s(duree.ms.)                 2.613  3.155 4.432  0.00315 ** 
## ti(measurement.no,duree.ms.) 3.274  4.240 7.847 2.48e-06 ***
## s(measurement.no):ton.ord2   1.001  1.002 1.433  0.23173    
## s(measurement.no):ton.ord3   1.001  1.002 0.023  0.88142    
## s(measurement.no):ton.ord4   1.002  1.003 0.342  0.56017
plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 170. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; set to the value(s): 80. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.central.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
        ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).

ai.central.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
                              s(f0, bs="cr",k=6) +
                              ti(measurement.no, f0,k=6) +
                              s(measurement.no, by=ton.ord, bs="cr",k=6),
                         data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.f0)
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1808.72      25.82  70.057  < 2e-16 ***
## ton.ord2     -183.71      28.33  -6.485 1.74e-10 ***
## ton.ord3     -198.13      29.76  -6.658 5.86e-11 ***
## ton.ord4     -147.99      26.51  -5.582 3.48e-08 ***
## 
## Approximate significance of smooth terms:
##                              edf Ref.df     F  p-value    
## s(measurement.no)          1.001  1.002 9.506  0.00212 ** 
## s(f0)                      4.105  4.579 7.115 2.97e-06 ***
## ti(measurement.no,f0)      5.049  5.936 5.348 2.37e-05 ***
## s(measurement.no):ton.ord2 1.001  1.001 0.421  0.51700    
## s(measurement.no):ton.ord3 1.001  1.001 0.465  0.49561    
## s(measurement.no):ton.ord4 1.001  1.001 0.610  0.43499
plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
            rug=F, col="red")
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 100. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
            rug=F, col="orange", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 120. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
            rug=F, col="yellow", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 140. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
            rug=F, col="green", add=T)
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 180. 
##  * NOTE : No random effects in the model to cancel.
## 
plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
            rug=F, col="blue", add=T)

## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; set to the value(s): 200. 
##  * NOTE : No random effects in the model to cancel.
## 
fvisgam(ai.central.mas.f2.gam.f0, view=c("measurement.no","f0"),
        ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))
## Summary:
##  * ton.ord : factor; set to the value(s): 4. 
##  * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000. 
##  * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605. 
##  * NOTE : No random effects in the model to cancel.
## 
## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).